Subgroups — D₆₀ #1218

Order 120.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₅	C₂	1	2	yes	maximal, complemented
2	C₃×C₄×C₅	C₂	1	1	yes	maximal, characteristic, complemented
3	D₂₀	—	3	1	no	maximal, Hall
4	C₂×C₃×C₅	C₂²	1	1	yes	characteristic
5	D₁₅	—	2	2	no	—
6	D₁₂	—	5	1	no	maximal, Hall
7	C₂×D₅	—	3	2	no	—
8	C₄×C₅	D₃	1	1	yes	characteristic, complemented
9	C₃×C₅	D₄	1	1	yes	characteristic, complemented, Hall
10	C₂×D₃	—	5	2	no	—
11	C₃×C₄	D₅	1	1	yes	characteristic, complemented
12	C₂×C₅	C₂×D₃	1	1	yes	characteristic
13	D₅	—	6	2	no	—
14	D₄	—	15	1	no	Sylow
15	C₂×C₃	C₂×D₅	1	1	yes	characteristic
16	D₃	—	10	2	no	—
17	C₅	D₁₂	1	1	yes	characteristic, complemented, Sylow
18	C₂²	—	15	2	no	—
19	C₄	D₁₅	1	1	yes	characteristic, complemented
20	C₃	D₂₀	1	1	yes	characteristic, complemented, Sylow
21	C₂	—	30	2	no	—
22	C₂	C₂×D₁₅	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.